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We present a method to compute, quickly and efficiently, the mutualinformation achieved by an IID (independent identically distributed) complexGaussian input on a block Rayleigh-faded channel without side information atthe receiver. The method accommodates both scalar and MIMO (multiple-inputmultiple-output) settings. Operationally, the mutual information thus computedrepresents the highest spectral efficiency that can be attained using standardGaussian codebooks. Examples are provided that illustrate the loss in spectralefficiency caused by fast fading and how that loss is amplified by the use ofmultiple transmit antennas. These examples are further enriched by comparisonswith the channel capacity under perfect channel-state information at thereceiver, and with the spectral efficiency attained by pilot-basedtransmission.

Mutual Information of IID Complex Gaussian Signals on Block Rayleigh-faded Channels